n-Gorenstein分次投(内)射模  

n-Gorenstein graded projective(injective) modules

作　　者：袁倩 张文汇 张铭 YUAN Qian;ZHANG Wen-hui;ZHANG Ming(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China;Longgang Middle School,Dazu District,Chongqing 402360,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070 [2]重庆市大足区龙岗中学,重庆402360

出　　处：《山东大学学报（理学版）》2022年第2期31-37,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11861055)。

摘　　要：设G是一乘法群,R是G-分次环,引入n-Gorenstein分次投射模和n-Gorenstein分次内射模,讨论了2类模的同调性质,证明了如果分次R-模M满足n-G-gr-pd_(R)M=m<∞,则存在正合列0→K→G→M→0,其中G是n-Gorenstein分次投射R-模,pd_(R)K=m-1。Let G be a multiplicative group,R be a G-graded ring,n-Gorenstein graded projective and n-Gorenstein graded injective modules are introduced,the homological properties and the dimensions of the two types of modules are investigated.It is proved that if the graded R-module M satisfies n-G-gr-pd_(R)M=m<∞,then exists an exact sequence 0→K→G→M→0,where G is n-Gorenstein graded projective R-module and pd_(R)K=m-1.

关 键 词：分次环 n-Gorenstein分次投(内)射模 n-Gorenstein分次投(内)射维数 

分 类 号：O153.3[理学—数学]